Master
in Space Science and Technology
Thermal engineering
Isidoro Martínez
Master in Space Science and Technology UPM. Isidoro Martínez
1
Thermal engineering
•Thermodynamics
– Basics
• Energy and entropy
• Temperature and thermometry
• Variables: state properties, process functions
• Equations of state, simple processes
• Phase change
– Applied:
• Mixtures. Humid air (air conditioning)
• Thermochemistry (combustion)
• Heat engines (power generation)
• Refrigeration (cold generation)
• Thermal effects on materials and processes
• Thermofluiddynamic flow 1D…
•Heat transfer (conduction, convection, radiation, heat exchangers)
Master in Space Science and Technology, UPM. Isidoro Martínez
2
Thermodynamics
•
Basic thermodynamics
– The science of heat and temperature. Work. Energy. Thermal energy.
– Energy and entropy. The isolated system. The traditional Principles
– Generalisation (mass, momentum, energy): the science of assets (conservatives
do not disappear) and spreads (conservatives tend to disperse)
– Type of thermodynamic systems (system, frontier, and surroundings)
• Isolated system: Dm=0, DE=0
• Closed system : Dm=0, DE0
• Open system : Dm0, DE0
– Type of thermodynamic variables
• Intensive or extensive variables
• State or process variables
– Type of thermodynamic equations
• Balance equations (conservation laws); e.g. DEclose-sys=W+Q
• Equations of state (constitutive laws); e.g. pV=mRT
• Equilibrium laws: S(U,V,ni)iso-sys(t) Smax e.g. dS/dU|V,ni=uniform…
• (Kinetics is beyond classical thermodynamics; e.g. q  kT )
•
Applied thermodynamics
Master in Space Science and Technology, UPM. Isidoro Martínez
3
Thermodynamics (cont.)
• Basic thermodynamics
• Applied thermodynamics
–
–
–
–
–
–
Energy and exergy analysis (minimum expense and maximum benefit)
Non-reactive mixtures (properties of real mixtures, ideal mixture model…)
Hygrometry (humid air applications: drying, humidification, air conditioning…)
Phase transition in mixtures (liquid-vapour equilibrium, solutions…)
Reactive mixtures. Thermochemistry. Combustion
Heat engines
• Gas cycles for reciprocating and rotodynamic engines
• Vapour cycles (steam and organic fluid power plants)
– Refrigeration, and heat pumps
• Cryogenics (cryocoolers, cryostats, cryopreservation…)
– Thermal analysis of materials (fixed points, calorimetry, dilatometry…)
– Non-equilibrium thermodynamics (thermoelectricity, dissipative structures…)
– Environmental thermodynamics (ocean and atmospheric processes…)
Master in Space Science and Technology, UPM. Isidoro Martínez
4
Balance equations
Magnitude
Accumul
.
mass
dm
=

momentum d(m v ) =
Production
energy
d(me)
=
0

mg dt
0
entropy
exergy
d(ms)
d(m)
=
=
dSgen
T0dSgen
Impermeable flux
+0

+ FA dt
+dW+dQ
+dQ/T
+dWu+(1T0/T)dQ
Permeable flux
+dme


+ ve dmepeAe ne dt
e+htedme
+sedme
+edme
with e=u+em=u+gz+v2/2
dW =IFFdx =IFMdq, Wu=W+ p0DV
h=u+pv, ht=h+em
ds=(du+pdv)/T =(dq+demdf)/T, demdf 0, dSgen0
=e+p0vT0s, =htT0s
Master in Space Science and Technology, UPM. Isidoro Martínez
5
Substance data
•
Perfect gas model
– Ideal gas: pV=mRT or pV=nRuT (R=Ru/M, Ru=8.3 J/(mol·K))
– Energetically linear in temperature: DU=mcvDT
–
•
Air data: R=287 J/(kg·K) and cp=cv+R=1000 J/(kg·K), or M=0.029 kg/mol and g=cp/cv=1.4
Perfect solid or liquid model
– Incompressible, undilatable substance: V=constant (but beware of dilatations!)
– Energetically linear in temperature: DU=mcDT
–
•
Water data: r=1000 kg/m3, c=4200 J(kg·K)
Perfect mixture (homogeneous)
v   xi vi , u   xiui , s   xi si  R xi ln xi
– Ideal mixture
– Energetically linear in temperature: DU=mcvDT
*
•
*
*
Heterogeneous systems
– Phase equilibria of pure substances (Clapeyron’s equation)
xV 1 p1* (T )
– Ideal liquid-vapour mixtures (Raoult’s law):

x
p
L1
– Ideal liquid-gas solutions (Henry’s law): cL,s  K sdis,cc (T )
•
dp
dT

sat
Dh
T Dv
cG , s
Real gases. The corresponding state model, and other equations of state.
Master in Space Science and Technology, UPM. Isidoro Martínez
6
Thermodynamic processes
•
Adiabatic non-dissipative process of a perfect gas:
dE  dQ  dW

•
•
 mcv dT  
mRT
dV
V
dT R dV

 0  Tvg 1  cte., pvg  cte., T/p
T cv V
g 1
g
 cte.
Fluid heating or cooling
–
–
•
 dU   pdV
At constant volume: Q=DU
At constant pressure: Q=DH=D(U+pV)
Adiabatic gas compression or expansion
–
Close system: w=Du=cv(T2-T1)
–
Open system: w=Dh=cp(T2-T1)
C 
ws h2ts  h1t


w h2t  h1t
PGM
 p2t
g 1
g
p1t   1
w PGM 1  T1t T2t
T 

g 1
T2t T1t  1
ws
1   p1t p2t  g
Internal energy equation (heating and cooling processes)
DU  DE  DEm  Q  Emdf   pdV
•
One-dimensional flow at steady state
min  mout  r vA  rV
•
Dh  w  q
Thermodynamic processes in engines
w
dp
r
 Dem  emdf
Master in Space Science and Technology, UPM. Isidoro Martínez
7
Phase diagrams (pure substance)
•
Normal freezing and boiling points (p0=100 kPa)
•
Triple point (for water TTR=273.16 K, pTR=611 Pa)
•
Critical point (for water TCR=647.3 K, pTR=22.1 MPa)
•
Clapeyron’s equation (for water hSL=334 kJ/kg, hLV=2260 kJ/kg)
dp
dT

sat
hV  hL
T (vV  v L )
FG p IJ  h FG 1  1 IJ
H p K R HT T K
V  v L , vV  RT / p , hLV  const
v
 ln
LV
0
Master in Space Science and Technology, UPM. Isidoro Martínez
0
8
Thermometry
• Temperature, the thermal level of a system, can be
measured by different primary means:
–
–
–
–
–
T
pV
 lim
The ideal-gas, constant-volume thermometer
TTPW p 0  pV TPW
The acoustic gas thermometer
1/ 4
The spectral radiation thermometer


T
M

lim


The total radiation thermometer
TTPW  1  M TPW 
The electronic noise thermometer
• The temperature unit is chosen such that TTPW  273.16 K
• The Celsius scale is defined by T/ºC  T/K-273.15
• Practical thermometers:
– Thermoresistances (e.g. Pt100, NTC)
– Thermocouples (K,J…).
Master in Space Science and Technology, UPM. Isidoro Martínez
9
Piezometry
•
Pressure (normal surface force per unit normal area), is a scalar
magnitude measured by difference (in non-isolated systems; recall
free-body force diagrams).
•
Gauge and absolute pressure:
•
•
Pressure unit (SI) is the pascal, 1 Pa1 N/m2 (1 bar100 kPa)
PLM
Hydrostatic equation:
 
 p  p0  r g  z  z0 
dp

  r g   PGM
dp
p
dz




g

dz
RT

Vacuum (practical limit is about 10-8 Pa)
Pressure sensors: U-tube, Bourdon tube, diaphragm, piezoelectric…
•
•
Master in Space Science and Technology, UPM. Isidoro Martínez
10
Questions
(Only one answer is correct)
1.
The mass of air in a 30 litre vessel at 27 ºC and a gauge pressure of 187 kPa is about?
a)
b)
c)
d)
2.
When a gas in a 30 litre rigid vessel is heated from 50 ºC to 100 ºC, the pressure ratio: (final/initial):
a)
b)
c)
d)
3.
Cannot be compressed
Cannot be heated by compression
Heat a little bit when compressed, but volume remains the same
Heat up and shrink when compressed
The critical temperature of any gas is:
a)
b)
c)
d)
5.
Doubles
Is closer to 1 than to 2.
Depends on initial volume
Depends on heating speed
Liquids:
a)
b)
c)
d)
4.
1g
10 g
100 g
1000 g..
The temperature below which the gas cannot exist as a liquid
-273.16 ºC
The temperature above which the gas cannot be liquefied
The temperature at which solid, liquid, and gas coexist
In a refrigerator, the amount of heat extracted from the cold side:
a)
b)
c)
d)
Cannot be larger than the work consumed
Cannot be larger than the heat rejected to the hot side
Is inversely proportional to the temperature of the cold side
Is proportional to the temperature of the cold side.
Master in Space Science and Technology, UPM. Isidoro Martínez
11
Questions
(Only one answer is correct)
6.
Which of the following assertions is correct?
a)
b)
c)
d)
7.
The variation of entropy in a gas when it is compressed in a reversible way is:
a)
b)
c)
d)
8.
Is always positive
Is dimensionless
Is different in the Kelvin and Celsius temperature scales
Is three times the linear coefficient value.
It is not possible to boil an egg in the Everest because:
a)
b)
c)
d)
10.
Less than zero
Equal to zero
Greater than zero
It depends on the process.
The volumetric coefficient of thermal expansion:
a)
b)
c)
d)
9.
Heat is proportional to temperature
Heat is a body’s thermal energy
Net heat is converted to net work in a heat engine
The algebraic sum of received heats in an interaction of two bodies must be null.
The air is too cold to boil water
Air pressure is too low for stoves to burn
Boiling water is not hot enough
Water cannot be boiled at high altitudes.
When a combustion takes place inside a rigid and adiabatic vessel:
a)
b)
c)
d)
Internal energy increases
Internal energy variation is null
Energy is not conserved
Heat flows out.
Master in Space Science and Technology, UPM. Isidoro Martínez
12
Exercises
1.
A U-tube is made by joining two 1 m vertical glass-tubes of 3 mm bore (6 mm
external diameter) with a short tube at the bottom. Water is poured until the
liquid fills 600 mm in each column. Then, one end is closed. Find:
1.
2.
2.
3.
4.
An aluminium block of 54.5 g, heated in boiling water, is put in a calorimeter
with 150 cm3 of water at 22 ºC, with the thermometer attaining a maximum of
27.5 ºC after a while. Find the thermal capacity of aluminium.
How many ice cubes of 33 g each, at -20 ºC, are required to cool 1 litre of tea
from 100 ºC to 0 ºC?
Carbon dioxide is trapped inside a vertical cylinder 25 cm in diameter by a
piston that holds internal pressure at 120 kPa. The plunger is initially 0.5 m
from the cylinder bottom, and the gas is at 15 ºC. Thence, an electrical heater
inside is plugged to 220 V, and the volume increases by 50% after 3 minutes.
Neglecting heat losses through all walls, and piston friction, find:
1.
2.
5.
The change in menisci height due to an ambient pressure change, (∂z/∂pamb), with
application to Dp=1 kPa.
The change in menisci height due to an ambient temperature change, (∂z/∂Tamb),
with application to DT=5 ºC.
The energy balance for the gas and for the heater.
The final temperature and work delivered or received by the gas.
Find the air stagnation temperature on leading edges of an aircraft flying at
2000 km/h in air at -60 ºC.
Master in Space Science and Technology, UPM. Isidoro Martínez
13
Master
in Space Science and Technology
Thermal engineering
Isidoro Martínez
Master in Space Science and Technology UPM. Isidoro Martínez
14
Thermal engineering
•Thermodynamics
–Basic (energy and entropy, state properties, state equations, simple
processes, phase changes)
–Applied (mixtures, liquid-vapour equilibrium, air conditioning,
thermochemistry, power and cold generation, materials processes)
•Heat transfer
–
–
–
–
–
–
–
Thermal conduction (solids…)
Thermal convection (fluids…)
Thermal radiation (vacuum…)
Heat exchangers
Heat generation (electrical heaters…)
Thermal control systems
Combined heat and mass transfer (evaporative cooling, ablation…)
Master in Space Science and Technology, UPM. Isidoro Martínez
15
Heat transfer
•
What is heat (i.e. heat flow, heat transfer)?
– First law: heat is non-work energy-transfer through an impermeable surf.
Q  DE  W  DE   pdV  Wdis DH   Vdp  Wdis   mcDT PIS,non-dis
– Second law: heat tends to equilibrate the temperature field.
sgen 
•
T  q
T2
What is heat flux (i.e. heat flow rate, heat transfer rate)?
dQ
dT
Q
 mc
dt
dt
•
 KADT
PSM,non-dis
Heat transfer is the flow of thermal energy driven by thermal nonequilibrium (i.e. the effect of a non-uniform temperature field),
commonly measured as a heat flux (vector field).
Master in Space Science and Technology, UPM. Isidoro Martínez
16
Heat transfer modes
•
How is heat flux density modelled?
conduction q  k T

Q
q   K DT convection q  h T  T 
A

4
4
radiation
q


T

T

 

– The 3 ways to change Q: K, A, and DT.
– K is thermal conductance coeff. (or heat transfer coeff.), k is conductivity,
h is convective coeff.,  is emissivity.
– Field or interface variables?
– Vector or scalar equations?
– Linear or non-linear equations?
– Material or configuration properties?
– Which emissivity? This form only applies to bodies in large enclosures.
Master in Space Science and Technology, UPM. Isidoro Martínez
17
Heat conduction
•
Physical transport mechanism
–Short-range atomic interactions (collision of particles in fluids, or phonon
waves in solids), supplemented with free-electron flow in metals.
•
Fourier’s law (1822)
q  kT
•
Heat equation
dH
dt
Q 
p
 rc
V
T
dV    q  ndA    dV      q dV    dV
t
A
V
V
V
k  0
T

 rc
   q    k  2T   , or
t
V 0
T

 a 2T 
t
rc
–with the initial and boundary conditions particular to each problem.
Master in Space Science and Technology, UPM. Isidoro Martínez
18
Thermal conductivity
Table 1. Representative thermal conductivity values
k [W/(m·K)]
Comments
Order of magnitude for solids 10 (good conductors) In metals, Lorentz's law (1881), k/(T)=constant
1 (bad conductors)
Aluminium
200
Duralumin has k=174 W/(m·K),
increasing to k=188 W/(m·K) at 500 K.
Iron and steel
50 (carbon steel)
Increases with temperature.
20 (stainless steel)
Decreases with alloying
Order of magnitude for liquids
1 (inorganic)
Poor conductors (except liquid metals).
0.1 (organic)
Water
0.6
Ice has k=2.3 W/(m·K),
2
Order of magnitude for gases
10
Very poor thermal conductors.
KTG predicts k/(rc)a=Di=10-5 m2/s
Air
0.024
Super insulators must be air evacuated.
2
Master in Space Science and Technology, UPM. Isidoro Martínez
19
Simple heat conduction cases
•
One-dimensional steady cases
– Planar
– Cylindrical
– Spherical
•
•
Q  kA
T1  T2
L12
Q  k 2 L
Q  k 4 R1R2
T1  T2
R2  R1
T1  T2
R
ln 2
R1
Composite wall (planar multilayer)
T T
T T
T T
q  K DT  k12 2 1  k23 3 2  ...  n 1
Li
L12
L23
k
i
Unsteady case. Relaxation time:
 Bi 1 r cL2
Dt  k
hL
Dt  mcDT / Q 
Bi 
Bi 1 r cV
kS
Dt 

hA
Master in Space Science and Technology, UPM. Isidoro Martínez
 K
1
Li
k
i
20
Multiple path in heat conduction
• Multidimensional analysis
– Analytical, e.g. separation of variables, conduction shape factors,
– Numerical, finite differences, lumped network, finite elements
• Parallel thermal resistances
– Example: honeycomb panel made of ribbon (thickness d), cell size s:
DT
Qx  kFx Ax x
Lx
Qy  kFy Ay
Qz  kFz Az
DTy
Ly
DTz
Lz
Master in Space Science and Technology, UPM. Isidoro Martínez
3d
with Fx 

2 s
d 
with Fy 

s 
8d 

with Fz 
3 s 
21
Heat convection
• Newton’s law and physical mechanism
q  h T  T   knT
•
•
 hDT  k
DT
d
 Nu 
hL
 f  Re,Pr...
k
W/(m2·K)
e.g. in air flow, h=a+bvwind, with a=3
and b=3 J/(m3·K)
e.g. plate (<1 m)at rest, h=a(T-T)1/4, with a2 W/(m2·K5/4) (1,6 upper, 0.8 lower, 1.8 vert.)
• Classification of heat convection problems
–
–
–
–
–
By time change: steady, unsteady (e.g. onset of convection)
By flow origin: forced (flow), natural (thermal, solutal…)
By flow regime: laminar, turbulent
By flow topology: internal flow, external flow
By flow phase: single-phase or multi-phase flow
• Heat exchangers (tube-and-shell, plates…)
• Heat pipes
Master in Space Science and Technology, UPM. Isidoro Martínez
22
Heat radiation
•
Heat radiation (thermal radiation)
– It is the transfer of internal thermal energy to electromagnetic field energy, or
viceversa, modelled from the basic black-body theory. Electromagnetic radiation is
emitted as a result of the motion of electric charges in atoms and molecules.
•
Blackbody radiation
– Radiation within a vacuum cavity
•
•
•
•
Radiation temperature (equilibrium with matter)
Photon gas (wave-particle duality, carriers with zero rest mass, E=h, p=E/c)
Isotropic, unpolarised, incoherent spatial distribution
Spectral distribution of photon energies at equilibrium (E=const., S=max.)
– Radiation escaping from a hole in a cavity
• Blackbody emmision
2 hc 2
M 

 hc
 5 exp 
 k T

 
  1
 

W

4
8
M

M
d



T


5.67·
10
0 

m2  K 4

C


C  0.003 m  K
 M   max T
Master in Space Science and Technology, UPM. Isidoro Martínez
23
Thermo-optical properties
• Propagation through real media
– Attenuation by absorption and scattering (Rayleigh if d<<, Mie if d)
• Properties of real surfaces
– Partial absorption (a), reflectance (r), emissivity (), and, in some
cases, transmittance (t). Energy balance: art=1.
– Directional and spectral effects (e.g. retroreflective surfaces, selective
glasses…)
– Detailed equilibrium: Kirchhoff's law (1859), aqT=qT, but usually a≠
• Spectral and directional modelling
– Two-spectral-band model:
– Diffuse (cosine law) or specular models
• Radiative coupling
•
 T14   T24
– e.g. planar infinite surfaces: q12  1  1
1 2
1
1
2
cos 1 cos  2
1
dA1dA2
View factors F12 
 A1 A2 A1
r122
Master in Space Science and Technology, UPM. Isidoro Martínez
24
Heat transfer goals
•
Analysis
–Find the heat flux for a given set-up and temperature field
e.g. Q  kA T  T / L

1
2

–Find the temperature corresponding to a given heat flux and set-up
e.g. T  T  QL /  kA) 
1
•
2
Design
–Find an appropriate material that allows a prescribed heat flux with a given T-field in a given
geometry
e.g.
k  QL /  ADT 
–Find the thickness of insulation to achieve a certain heat flux with a given T-field in a prescribed
geometry
e.g. L  kA T  T  / Q
1
•
2
Control
-To prevent high temperatures, use insulation and radiation shields, or use heat sinks and coolers.
–To prevent low temperatures, use insulation and radiation shields, or use heaters.
–To soften transients, increase thermal inertia (higher thermal capacity, phase change materials).
Master in Space Science and Technology, UPM. Isidoro Martínez
25
Application to electronics cooling
• All active electrical devices at steady state must evacuate the
energy dissipated by Joule effect (i.e. need of heat sinks).
• Most electronics failures are due to overheating (e.g. for germanium
at T>100 ºC, for silicon at T>125 ºC).
• At any working temperature there is always some dopant diffusion at
junctions and bond-material creeping, causing random electrical
failures, with an event-rate doubling every 10 ºC of temperature
increase. Need of thermal control.
• Computing power is limited by the difficulty to evacuate the energy
dissipation (a Pentium 4 CPU at 2 GHz in 0.18 mm technology must
dissipate 76 W in an environment at 40 ºC without surpassing 75 ºC
at the case, 125 ºC at junctions).
• Modern electronic equipment, being powerfull and of small size,
usually require liquid cooling (e.g. heat pipes).
Master in Space Science and Technology, UPM. Isidoro Martínez
26
Thermal modelling
• Modelling the geometry
• Modelling the material properties
• Modelling the transients
• Modelling the heat equation
• Mathematical solution of the model
– Analytical solutions
– Numerical solutions
• Analysis of the results
• Verification planning (analytical checks and testing)
• Feedback
Master in Space Science and Technology, UPM. Isidoro Martínez
27
Questions
(Only one answer is correct)
1.
The steady temperature profile in heat transfer along a compound wall:
a)
b)
c)
d)
2.
If the temperature at the hot side of a wall is doubled:
a)
b)
c)
d)
3.
It loses and gains heat at the same rate
The heat absorbed equals its thermal capacity
It reflects all the energy that strikes it
No more heat is absorbed.
A certain blackbody at 100 ºC radiates 100 W. How much radiates at 200 ºC?
a)
b)
c)
d)
5.
Heat flow through the wall doubles
Heat flow through the wall increases by a factor of 4
Heat flow through the wall increases by a factor of 8
None of the above.
When a piece of material is exposed to the sun, its temperature rises until:
a)
b)
c)
d)
4.
Has discontinuities
Must have inflexion points
Must be monotonously increasing or decreasing
Must have a continuous derivative.
200 W
400 W
800 W
None of the above.
When two spheres, with same properties except for their radius, are exposed to the Sun and empty
space:
a)
b)
c)
d)
The larger one gets hotter
The larger one gets colder
The larger one gets hotter or cooler depending on their emissivity-to-absorptance ratio
None of the above.
Master in Space Science and Technology, UPM. Isidoro Martínez
28
Exercises
1.
2.
3.
4.
5.
A small frustrum cone 5 cm long, made of copper, connects two metallic plates, one at 300 K in
contact with the smallest face, which is 1 cm in diameter, and the other at 400 K, at the other
face, which is 3 cm in diameter. Assuming steady state, quasi-one-dimensional flow, and no
lateral losses, find:
–
The temperature profile along the axis.
–
The heat flow rate.
An electronics board 100·150·1 mm3 in size, made of glass fibre laminated with epoxy, and
having k=0.25 W/(m·K), must dissipate 5 W from its components, which are assumed uniformly
distributed. The board is connected at the largest edges to high conducting supports held at 30
ºC. Find:
1. The maximum temperature along the board, if only heat conduction at the edges is accounted for
(no convection or radiation losses).
2. The thickness of a one-side copper layer (bonded to the glass-fibre board) required for the
maximum temperature to be below 40 ºC above that of the supports.
3. The transient temperature field, with and without a convective coefficient of h=2 W/(m2·K).
Find the required area for a vertical plate at 65 ºC to communicate 1 kW to ambient air at 15 ºC.
Consider two infinite parallel plates, one at 1000 ºC with =0.8 and the other at 100 ºC with =0.7.
Find:
–
The heat flux exchanged.
–
The effect of interposing a thin blackbody plate in between.
Find the steady temperature at 1 AU, for an isothermal blackbody exposed to solar and
microwave background radiation, for the following geometries: planar one-side surface (i.e.
rear insulated), plate, cylinder, sphere, and cube.
(END)
Master in Space Science and Technology, UPM. Isidoro Martínez
29
Referencias
• http://webserver.dmt.upm.es/~isidoro/
• Martínez, I., "Termodinámica básica y aplicada",
Dossat, 1992.
• Wark, K., "Thermodynamics", McGraw-Hill, 1999.
Versión española Edit. McGraw-Hill, 2000.
• Holman, J.P., "Heat transfer", McGraw-Hill, 2010.
• Gilmore, D.G., “Satellite Thermal Control Handbook”,
The Aerospace Corporation Press, 1994.
• www.electronics-cooling.com
Master in Space Science and Technology, UPM. Isidoro Martínez
30